We consider hexahedral elements with continuous piecewise trilinear shape functions. The geometry in the experiments is the complex body depicted in Figure REF , which is often considered in the literature of immersed finite element methods; see [1]}. The bounding box used to define the background mesh is the unit cube \([0, 1]^3\) , which is also depicted in Figure REF . We consider background meshes of hexahedral elements generated and partitioned in parallel with the \(\mathtt {p4est}\)  library. The test is performed for three different local loads (referred to as “load 1", “load 2" and “load 3") with \(20^3\) , \(30^3\) , and \(40^3\)  elements per parallel subdomain, respectively. We generate the meshes by recursive subdivision of the unit cube. The finest mesh considered in the examples has \(1,073,741,824\)  elements (corresponding to refinement level 10), and it is partitioned into \(16,777\)  subdomains which are mapped to the same number of MPI tasks.
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